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Conductive Atomic Force Microscopy:
Applied and Modeled
 Samuel Emmons, Dr. Doug Dunham
 Physics, Materials Science
Introduction:
 University of Wisconsin-Eau Claire
The Problem:
What is an Atomic Force Microscope?
The Solution (cont.)
Qualitative vs. Quantitative:
Current vs. Voltage on Hard Disk
Current (A)
An Atomic Force Microscope, or AFM, is a research
instrument in the Scanning Probe Microscope, or SPM,
family of instruments. An SPM is any device which
probes or examines certain characteristics of a sample
surface being studied. For example, Optical
microscopes use visible light (photons) to examine
surfaces and specimen. Electron Microscopes probe
the sample surface with a beam of electrons to observe
physical features and properties. Atomic Force
Microscopes use a very sharp tip attached to a lever
arm (cantilever) to probe a range of sample
characteristics at the micro and nano-scale. The tip is
kept very close to the surface and scans across the
sample, essentially “feeling” the surface.
2.50E-008
2.00E-008
1.50E-008
1.00E-008
5.00E-009
Voltage(V)
0.00E+000
-15
-10
-5
0
5
10
-5.00E-009
Basic AFM Schematic
As the tip moves back and forth across the
sample a laser is reflected off of the top of
the cantilever and onto a photo-detector. An
electronic feedback loop works to keep
constant a prescribed situation detected by
the photo-detector. (See below**)
A Variety of Operating Modes:
**The most basic use of the AFM is to generate an image of sample topography, i.e. to see
what the surface looks like. This is typically done in two modes, each of which maintains a
prescribed condition on the photo-detector. One of the two, called Contact Mode, maintains a
constant cantilever deflection, meaning it keeps the reflected laser beam at the same spot on
the photo-detector. It does so by moving the tip/cantilever assembly up and down with a
piezoelectric actuator connected to some feedback electronics. The distance the assembly
moves is thus the height of the feature the tip is passing over. The other is AC, or Oscillating,
Mode, in which the cantilever is driven at its natural thermal resonance frequency. The
prescribed condition kept constant in this case is the amplitude of the oscillation detected by
the photo-detector, and this is accomplished using the same piezoelectric actuator.
-1.00E-008
-1.50E-008
-2.00E-008
15
A Comparison:
While AFM topography can
provide quantitative sample
data, Conductive AFM
provides only qualitative data.
This is a difficult problem to
overcome. In the constant
sample voltage/scanning tip
mode CAFM provides current
data across the topography of
the sample, so one may see
what regions conduct more
than others. Current vs.
Voltage data is also largely
qualitative. The question is
how to make these
measurements quantitative.
A useful comparison may be made
when considering the case when direct
current can pass between the tip and
the sample. In theory there is thus a
capacitance and resistance in parallel
between the tip and the sample surface
in addition to the sample resistance.
Therefore a parallel RC Circuit analysis
is a helpful point of comparison for real
data, such as the Current vs. Voltage
data given in the slide to the left for a
Hard Disk.
Parallel RC Circuit:
AC
Note the similarity between this curve and the Hard
Disk curve at left. The dissimilarities come from the
oxide layer and amplifier effects in the real data.
-2.50E-008
This is real current data from a Current vs. Voltage measurement. The +10V/-10V oscillation is applied to the
sample as a triangle wave. Note how the current reaches a maximum and minimum current magnitude of
2.0E-008A, or 20nA. This is not a result of the sample but a limitation of the current signal amplifier used in
the AFM. There are a couple of other issues that make analysis of this data difficult. One is the unknown
combined sample and tip to sample resistance, and another is the unknown tip to sample capacitance. The
curve flatness at 0V is also difficult to analyze, and it is likely due to a thin surface oxide layer.
The Solution:
Knowing the Unknowns:
Model Parallel RC Circuit
A Simple Model:
In order to further extrapolate unknown variables it is helpful to have a simple model
of the Conductive AFM tip over the sample. To build this, I have modeled the tip as a
cone and the sample as a plane beneath. The situation in consideration is for a
constant potential V0 placed on the sample surface with the tip at 0V. This is, of
course, an approximation because in reality there would be a voltage drop across the
sample. The target variable that we are seeking here is the tip to sample capacitance.
A Boundary Value Problem
A significant step forward in quantitative AFM is to narrow down and extrapolate out
unknown variables. The primary unknown variables are the tip to sample capacitance (i.e.
between the tip and the sample surface), the sample resistance, and the tip to sample
resistance. To identify these variables it is helpful to construct some equivalent electrical
circuits that model Conductive AFM operation. The two primary useful circuits are a parallel
RC (Resistor/Capacitor) circuit and a series RC circuit.
With this model of the tip on the sample we may attempt
to calculate the capacitance of the tip/sample model.
The best way to do this is to first find the potential
function. A preferred method in this case is to work
through a boundary valued problem in cylindrical
coordinates with Laplace’s equation. The differential
equation is given here:
Model tip for CAFM
15 mm
4 mm
Equation for RC Constant
Here b1 is the value of the semi-minor axis corresponding
to angular frequency u and b2 is the value of the semi
minor axis corresponding to angular frequency w.
Because we see that there is no polar angle
dependence, the derivative with respect to phi is 0. It is
also common to have a separable solution when dealing
with Laplace’s equation, so that’s the solution guess:
The differential equation becomes:
AFM Topography/Lithography
Magnetic Force Microscopy
This is an image of the UWEC seal
which I etched into a polycarbonate
surface. The height difference from
light(high) to dark(low) is about 30nm.
The image seen above is the magnetic
domain structure of a 16 square
micron segment of a Hard Disk, taken
in the Magnetic Force Mode of AFM.
Current vs. Voltage on P-type Silicon
When the metal coated CAFM tip is in contact with the
surface a Metal Oxide Semiconductor (MOS) Capacitor is
formed, completing a series RC Circuit.
Series RC Current vs. Voltage Curve
Conductive Atomic Force Microscopy :
Topography of Hard Disk
A Hard Disk is a good test sample for CAFM because it is
highly conductive. This image is a little less than 3 microns
wide, and has about a 5nm range in height. The color was
added to the image to increase contrast.
Conductive Atomic Force
Microscopy, or CAFM, refers to the
mode of AFM operation in which a
current is passed through the
tip/sample connection to determine
the conductive properties of a
sample surface. There are two
relatively easy ways of determining
these conductive properties. One is
to maintain a constant voltage on the
sample and move the tip, resulting in
a variety of currents measured
dependent on tip location on the
sample. The other is by keeping the
tip position constant and varying the
voltage on the surface, thus
obtaining current vs. voltage data for
a specific point on the sample.
The general solutions for R(r) and Z(z) are:
Here J0 is a Bessel Function of the first kind, and Y0 is a
Bessel Function of the second kind. I have yet to apply the
boundary conditions (given potential info.) to this solution.
When the tip and sample connection cannot
pass direct current between them, the circuit
acts as a series RC circuit, where the
resistance is the sample resistance and the
capacitance is the tip to sample capacitance.
The above curve was made in Maple. First, I
solved the associated differential equation
for charge as a function of time, Q(t).
The differential equation is:
b2
Future Development:
Complete Model:
Completing the model will allow for the implementation of the theory to a real sample.
This sample would likely be a cleaned Silicon substrate with approximately known
sample resistance, so that the accuracy of the capacitance model may be determined.
R*(dQ(t)/dt)+Q(t)/C = V*cos(w*t)
where w is the angular frequency at which
the sample voltage is driven. Taking the time
derivative of the solution Q(t) gives the
current, I(t), which, plotted against voltage,
yields the above curve. Noticing that this is
an ellipse, it turns out that knowing the value
of the semi-major and semi-minor axes for
two values of w allows one to solve for the
value of R multiplied by C, or RC.
This model was created in Maple. As is
evident, the tip has been modeled as a cone
and the surface as an infinite plane.
b1
Sample Application:
Once the model is finessed, it may be applied to certain fabricated samples to
determine if the electrical properties of the actual sample closely match expected
values.
RC Value on P-type Silicon
w=4pHz; u=2pHz; b1=8.1E-11A; b2=1.49E-10A
RC=0.159s approximately.
Acknowledgements:
 UWEC Materials Science Center